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Mimetic discretizations for Maxwell’s equations. (English) Zbl 0956.78015
Summary: The authors have constructed reliable finite difference methods for approximating the solution to Maxwell’s equations using accurate discrete analogs of differential operators that satisfy the identities and theorems of vector and tensor calculus in discrete form. The numerical approximation does not have spurious modes and mimics many fundamental properties of the underlying physical problem including conservation laws, symmetries in the solution, and the nondivergence of particular vector fields. Numerical examples demonstrate the high quality of the method when the medium is strongly discontinuous and for nonorthogonal, nonsmooth computational grids.
MSC:
78M20Finite difference methods (optics)
78A25General electromagnetic theory